A Doubly Robust Approach to Sparse Reinforcement Learning

Wonyoung Kim, Garud Iyengar, Assaf Zeevi
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2305-2313, 2024.

Abstract

We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min}s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-kim24c, title = {A Doubly Robust Approach to Sparse Reinforcement Learning}, author = {Kim, Wonyoung and Iyengar, Garud and Zeevi, Assaf}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2305--2313}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/kim24c/kim24c.pdf}, url = {https://proceedings.mlr.press/v238/kim24c.html}, abstract = {We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min}s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.} }
Endnote
%0 Conference Paper %T A Doubly Robust Approach to Sparse Reinforcement Learning %A Wonyoung Kim %A Garud Iyengar %A Assaf Zeevi %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-kim24c %I PMLR %P 2305--2313 %U https://proceedings.mlr.press/v238/kim24c.html %V 238 %X We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min}s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.
APA
Kim, W., Iyengar, G. & Zeevi, A.. (2024). A Doubly Robust Approach to Sparse Reinforcement Learning. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2305-2313 Available from https://proceedings.mlr.press/v238/kim24c.html.

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